Definitely avoid the Bay if you can, as a rule everything there is overrated, overpriced, and generally pretty disappointing.
I second the suggestion of Vegetarian Food Studio, it is superb even for non-veggies like myself. Not your average Indian! Canteen on Clifton Street (on Clifton Street, funnily enough) is another good place for vegetarians that also caters for meat eaters.
Tenkaichi on City Road is great if you like sushi, and I've heard good things about Ichiban on Albany Road too.
Madame Fromage in the Castle Arcade is a great deli that sells the best baguettes in Cardiff without question. Expect to wait for it, but it's worth the wait, and worth every penny of the seemingly expensive price.